A universal measure of the conformity of a mesh with respect to an anisotropic metric field

In this paper, a method is presented to measure the non-conformity of a mesh with respect to a size specification map given in the form of a Riemannian metric. The measure evaluates the difference between the metric tensor of a simplex of the mesh and the metric tensor specified on the size specification map. This measure is universal because it is a unique, dimensionless number which characterizes either a single simplex of a mesh or a whole mesh, both in size and in shape, be it isotropic or anisotropic, coarse or fine, in a small or a big domain, in two or three dimensions. This measure is important because it can compare any two meshes in order to determine unequivocally which of them is better. Analytical and numerical examples illustrate the behaviour of this measure